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Is there a point of $ \omega\sp *$ that sees all others?


Author: Neil Hindman
Journal: Proc. Amer. Math. Soc. 104 (1988), 1235-1238
MSC: Primary 04A20; Secondary 03E05, 54D35
DOI: https://doi.org/10.1090/S0002-9939-1988-0931732-9
MathSciNet review: 931732
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Abstract | References | Similar Articles | Additional Information

Abstract: If the cardinal $ c$ of the continuum is singular and $ p$ is an ultrafilter on $ \omega $ of character $ c$, then there is an ultrafilter $ q$ on $ \omega $ which is not comparable to $ p$ in the Rudin-Keisler order.


References [Enhancements On Off] (What's this?)

  • [1] W. W. Comfort, Ultrafilters: an interim report, Surveys in general topology, Academic Press, New York-London-Toronto, Ont., 1980, pp. 33–54. MR 564099
  • [2] W. W. Comfort and S. Negrepontis, The theory of ultrafilters, Springer-Verlag, New York-Heidelberg, 1974. Die Grundlehren der mathematischen Wissenschaften, Band 211. MR 0396267
  • [3] D. Fremlin, Consequences of Martin's Axiom, Cambridge Univ. Press, Cambridge, 1984.
  • [4] K. Kunen, Weak 𝑃-points in 𝑁*, Topology, Vol. II (Proc. Fourth Colloq., Budapest, 1978) Colloq. Math. Soc. János Bolyai, vol. 23, North-Holland, Amsterdam-New York, 1980, pp. 741–749. MR 588822
  • [5] Jan van Mill, An introduction to 𝛽𝜔, Handbook of set-theoretic topology, North-Holland, Amsterdam, 1984, pp. 503–567. MR 776630
  • [6] Walter Rudin, Homogeneity problems in the theory of Čech compactifications, Duke Math. J. 23 (1956), 409–419. MR 0080902
  • [7] S. Shelah and M. E. Rudin, Unordered types of ultrafilters, Proceedings of the 1978 Topology Conference (Univ. Oklahoma, Norman, Okla., 1978), I, 1978, pp. 199–204 (1979). MR 540490

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1988-0931732-9
Keywords: Ultrafilters, Rudin-Keisler order
Article copyright: © Copyright 1988 American Mathematical Society